Numerical simulation of the steady-state Herschel–Bulkley fluid flow in a channel with sudden expansion

In this paper, the steady-state flow of a non-Newtonian fluid in a planar channel with sudden expansion is investigated. The rheological behavior of this media is described by the Herschel–Bulkley model. To determine the static velocity and pressure fields, a numerical algorithm based on the relaxation method and SIMPLE procedure are used. The MPI technique of parallel programming is used to accelerate the computation. Regularization of the rheological model is used to provide algorithm stability and limit viscosity increase at low deformation rates.
The mathematical problem statement involves non-dimensional parameters: the Reynolds number, Bingham number (non-dimensional viscoplasticity parameter), and power-law index. We report results of numerical simulation in a range of $1 \leqslant \mathrm{Re} \leqslant 40$ for the Reynolds number, $0 \leqslant \mathrm{Se} \leqslant 2$ for the Bingham number, and $0.4 \leqslant k \leqslant 2$ for the power-law index (shear thinning and shear thickening fluids).
Main characteristic distribution of the fluid flow with a two-dimensional localization in the expansion zone is presented. The impact of main parameters of the problem on the dead zone distribution in the fluid flow is shown.